No abstract

The Sierpinski gasket (also known as the Sierpinski triangle) is one of the fundamental models of self-similar sets. There have been many studies on different features of this set in the last decades. In this paper, initially we construct a dynamical system on the Sierpinski gasket by using expanding and folding maps. We then obtain a surprising shift map on the code set of the Sierpinski gasket, which represents the dynamical system, and we show that this dynamical system is chaotic on the code set of the Sierpinski gasket with respect to the intrinsic metric. Finally, we provide an algorithm to compute periodic points for this dynamical system.

In this paper, it is aimed to construct two different dynamical systems on the Sierpinski tetrahedron. To this end, we consider the dynamical systems on a quotient space of $\{ 0,1,2,3 \}^{\mathbb{N}}$ by using the code representations of the points on the Sierpinski tetrahedron. Finally, we compare the periodic points to investigate topological conjugacy of these dynamical systems and we conclude that they are not topologically equivalent.

In this paper, we …rst de…ne an equivalence relation on the sequence space 2 . Then we equip the quotient set 2 = with a metric d 1 . We also determine an isometry map between the metric spaces ( 2 = ; d 1 ) and ([0; 1]; d eucl ). Finally, we investigate the symmetry conditions with respect to some points on the metric space ( 2 = ; d 1 ) and we compare truncation errors for the computations which is obtained by the metrics d eucl and d 1 .

In this paper, our main aim is to obtain two different discrete chaotic dynamical systems on the Box fractal ($B$). For this goal, we first give two composition functions (which generate Box fractal and filled-square respectively via escape time algorithm) of expanding, folding and translation mappings. In order to examine the properties of these dynamical systems more easily, we use the intrinsic metric which is defined by the code representation of the points on $B$ and express these dynamical systems on the code sets of this fractal. We then obtain that they are chaotic in the sense of Devaney and give an algorithm to compute periodic points.